% This file generates the IRF presented in the sixth quadrant (2,3) in 
% Figure 9 in the paper. It needs to be ran from 
% 'FIG_9_Robustness_Output.m'.

global P2 lambda P H
%% Options for the specific results to generate.

graph           =   0;          % = 1 to generate a plot. 

csv_file        =   1;          % = 1 if you want to import from CSV.
                                % = 0 if you want to import from XLSX.

use_data        =   1;          % = 1   if baseline data
                                % = 3.1 if output is Industrial Production Index 
                                % = 3.3 if output is hours per capita nonfarm
                                % = 3.5 if output is unemployment rate.  
%% Importing and Preparing the data.

if csv_file == 1
    data            =   csvread('Data_File_Baseline.csv');
    % UM Expectations Median:     
    pilev_data      =   csvread('Data_File_Inflation.csv');
    pilev           =   pilev_data(:,6);     
else
    data            =   xlsread('Data_File.xlsx','Baseline');
    % UM Expectations Median:
    pilev           =   xlsread('Data_File.xlsx','Inflation','F2:F281');
end
% Import the specific variables. 
dz              =   data(:,3);
dy              =   data(:,4);
zlb             =   data(:,5);
rec             =   data(:,6);
zlev            =   data(:,7);
time            =   data(:,9);
[T,n]           =   size(dy);

if use_data == 1                % GDP
    ylev        =   data(:,8);      
elseif use_data ==  2        % IPI      
    ylev_data   =   csvread('Data_File_Output.csv');
    ylev        =   log(ylev_data(:,2));  
elseif use_data ==  3         % Hours
    ylev_data   =   csvread('Data_File_Output.csv');
    ylev        =   (ylev_data(:,6));  
elseif use_data ==  4          % Unemployment
    ylev_data   =   csvread('Data_File_Output.csv');
    ylev        =   log(ylev_data(:,8));  
end

% Defining the sample:
st              =   148;                    % = 1 for full sample 
                                            % = 148 for 1984Q1 
                                            % = 52 for 1960Q1. 

%% Options for local projections.

h1              =   1;      % For splines.        
lambda          =   100;    % Value of penalty of SLP.
r               =   3;      % r-1 = order of the limit polynomial for the SLP.

%% Main loop to generate IRFs.

Ps              =   [2; 3; 4];

for ix = 1:length(Ps)
    
    P                       =   Ps(ix);
    
    % LHS:
    ylev2                   =   ylev(st:end);
    % Productivity:
    zlev2                   =   zlev(st:end);
    % Inflation:
    pilev2                  =   pilev(st:end);
    % Dummy for ZLB:
    zlb2                    =   zlb(st:end);
    
    % Creating W matrix: 
    ff                      =   [ylev2 zlev2 pilev2];
    w                       =   lagmatrix(ff,1:P) ;     % Remove period t observations.

    % Creating lagged variables interacted with period-t ZLB dummy:
    [TY,YT]                 =   size(w);
    zlb3                    =   zeros(TY,YT);
    for jx = 1:YT
        zlb3(:,jx)              =   zlb2;
    end
    www                     =   zlb3.*w; 
    zlb4                    =   1- zlb3;
    wwww                    =   zlb4.*w;
    
    % LHS variable:   
    y                       =   ylev2(1+P:end,:); 
    
    % Local projection.
        % Standard case. 
    w                       =   [zlb2(1+P:end) zlb2(1+P:end).*zlev2(1+P:end),...
                                 wwww(1+P:end,:),www(1+P:end,:)]; 
    x                       =   (1-zlb2(1+P:end)).*zlev2(1+P:end,:);  % Shock variable. 
    lp                      =   locproj_var(y,x,w,h1,H,'reg'); 
    % Extract the IRF from local projection: 
    irf                     =   lp.IR(2:H+1); 
    % Construct standard errors:
    if st == 148
        u                   =   lp.Y - lp.X*lp.theta;
        [nwse_lp,vc_lp]     =   NeweyWest(u,lp.X,0,0);
    end
    % ZLB case.
    w                       =   [zlb2(1+P:end) (1-zlb2(1+P:end)).*zlev2(1+P:end,:),...
                                 wwww(1+P:end,:), www(1+P:end,:)];
    x                       =   zlb2(1+P:end).*zlev2(1+P:end);
    lp_zlb                  =   locproj_var(y,x,w,h1,H,'reg'); 
    % Extract the IRF from local projection:
    irf_zlb                 =   lp_zlb.IR(2:H+1); 
    % Construct standard errors:
    u                       =   lp_zlb.Y - lp_zlb.X*lp_zlb.theta;
    [nwse_lp_zlb,vc_lp_zlb] =   NeweyWest(u,lp_zlb.X,0,0);

    % Smooth local projection.
        % Standard case. 
    w                       =   [zlb2(1+P:end) zlb2(1+P:end).*zlev2(1+P:end),...
                                 wwww(1+P:end,:), www(1+P:end,:)]; 
    x                       =   (1-zlb2(1+P:end)).*zlev2(1+P:end,:); 
    slp                     =   locproj_var(y,x,w,h1,H,'smooth',r,lambda); 
	% Extract the IRF from local projection:
    irf_slp                 =   slp.IR(2:H+1);
    P2                      =   slp.P2;
    % Construct standard errors:
    if st == 148
        u                       =   slp.Y - slp.X*slp.theta;
        [nwse_slp,vc_slp,Q]     =   NeweyWest_slp(u,slp.X,0,0);
        V2                      =   slp.B*vc_slp(1:slp.K,1:slp.K)*slp.B';
        se_slp                  =   sqrt(diag(V2));
    end
        % ZLB case.
    w                       =   [zlb2(1+P:end) (1-zlb2(1+P:end)).*zlev2(1+P:end),...
                                 wwww(1+P:end,:), www(1+P:end,:)];
    x                       =   zlev2(1+P:end,:).*zlb2(1+P:end);
    slp_zlb                 =   locproj_var(y,x,w,h1,H,'smooth',r,lambda);
	% Extract the IRF from local projection:
    irf_slp_zlb             =   slp_zlb.IR(2:H+1);
    % Construct standard errors:
    if st == 148
        u                       =   slp_zlb.Y - slp_zlb.X*slp_zlb.theta;
        [nwse_slp_zlb,vc_slp_zlb]= NeweyWest_slp(u,slp_zlb.X,0,0);
        V22                     =   slp_zlb.B*vc_slp_zlb(1:slp_zlb.K,1:slp_zlb.K)*slp_zlb.B';
        se_slp_zlb              =   sqrt(diag(V22));
    end
    
    %% Saving results to Excel.
   
    p = 0.9;
    bb = tinv(p,TY-P);
    
    if P == 2
        irf_lp_P_2                  =   irf;
        irf_slp_P_2                 =   irf_slp;
        irf_lp_P_2_zlb              =   irf_zlb;        
        irf_slp_P_2_zlb             =   irf_slp_zlb;
        irf_slp_P_2_LB              =   (irf_slp-bb*se_slp(1:H));
        irf_slp_P_2_UB              =   (irf_slp+bb*se_slp(1:H));
        irf_lp_P_2_LB               =   (irf-bb*nwse_lp(1:H));
        irf_lp_P_2_UB               =   (irf+bb*nwse_lp(1:H));
    elseif P == 3
        irf_lp_P_3                  =   irf;        
        irf_slp_P_3                 =   irf_slp;
        irf_lp_P_3_zlb              =   irf_zlb;        
        irf_slp_P_3_zlb             =   irf_slp_zlb;
    elseif P == 4
        irf_lp_P_4                  =   irf;
        irf_slp_P_4                 =   irf_slp;
        irf_lp_P_4_zlb              =   irf_zlb;        
        irf_slp_P_4_zlb             =   irf_slp_zlb;
    end
end

%% Creating graph. 
     
t                       =   0:H-1;

if graph == 1
    figure
    plot(t,irf,'-k',t,irf_slp,'-b',t,irf_zlb,':k',t,irf_slp_zlb,':b','Linewidth',2)
    grid on 
    h = legend('LP','SLP','ZLB','ZLB SLP','Location','Best');
    set(h,'Interpreter','latex');
    if use_data == 1
        title('Output','Interpreter','latex')
    end
    if use_data == 2
        title('IP','Interpreter','latex')
    end   
    if use_data == 3
        title('Hours','Interpreter','latex')
    end 
    if use_data == 4
        title('Unemployment','Interpreter','latex')
    end 
    xlabel('$h$','Interpreter','latex')

    figure
    plot(t,(1/100)*irf_slp,'-b',t,(1/100)*irf_slp_zlb,':b','Linewidth',2)
    grid on 
    h = legend('SLP','ZLB SLP','Location','Best');
    set(h,'Interpreter','latex');
    if use_data == 1
        title('Output','Interpreter','latex')
    end
    if use_data == 2
        title('IP','Interpreter','latex')
    end   
    if use_data == 3
        title('Hours','Interpreter','latex')
    end 
    if use_data == 4
        title('Unemployment','Interpreter','latex')
    end 
    xlabel('$h$','Interpreter','latex')    
end